if the area of △ABC=92.5 Km^2, ∠C=73 degrees, abd b=16 km, then what is the length of a to the nearest km
To find the length of side a, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
Since we know the area (92.5 Km^2) and the base (b = 16 km), we can rearrange the formula to solve for the height:
Height = (2 * Area) / base
Height = (2 * 92.5 Km^2) / 16 km
Height = 11.56 km
Now, we can use this height and the given angle to find the length of side a using trigonometry.
In a right-angled triangle, the side opposite to the angle C is the height, and the side adjacent to angle C is side a.
Using the tangent function:
tan(angle) = opposite / adjacent
tan(73) = 11.56 km / a
To find a, we rearrange the formula:
a = 11.56 km / tan(73)
a ≈ 28.5 km (to the nearest km)
Therefore, the length of side a to the nearest km is 28 km.